Weighting in the imaging process is important, in order to improve the dynamic range and the
fidelity of a final aperture synthesized image. Each visibility sample is given a user
selected weight in the imaging step. This weighting can be used to account for differences
in the density of sampling in different parts of the 
plane. When gridding, N
visibilities contribute to a `summed' (really convolved and re-sampled) visibility in each
grid cell. Uniform weighting means that the gridded visibility is normalized by N; it is
weighted down by the local density of points. This means that each gridded cell contributes
`uniformly' to the Fourier transform. In natural weighting, the normalization by N is not
done, so that each gridded visibility contributes its `natural' weight to the Fourier
transform.
In natural weighting, visibilities for shorter spacings get higher weightage in the visibility data. Whereas, in uniform weighting, puts a zero weight where there are no measurements and a unit weight wherever there are measurements, independent of how many measurements contributed.